Skew braces of squarefree order

Abstract

Let n ≥ 1 be a squarefree integer, and let M, A be two groups of order n. Using our previous results on the enumeration of Hopf-Galois structures on Galois extensions of fields of squarefree degree, we determine the number of skew braces (up to isomorphism) with multiplicative group M and additive group A. As an application, we enumerate skew braces whose order is the product of three distinct primes, in particular proving a conjecture of Bardakov, Neshchadim and Yadav on the number of skew braces of order 2pq for primes q > p ≥ 3.